# Multistate reversible copolymerization of nonMarkovian chains under low conversion conditions

## TL;DR

This paper analytically solves the reversible multistate copolymerization kinetics under low conversion conditions, revealing how non-Markovian chain sequences are characterized by matrices linked to monomer units, affecting growth and thermodynamics.

## Contribution

It provides an analytical solution for the kinetics of multistate reversible copolymerization, introducing a matrix-based characterization of non-Markovian sequence properties.

## Key findings

- Matrices determine growth velocity and sequence statistics.
- Non-Markovian sequences are characterized by state-dependent matrices.
- Thermodynamics of copolymerization are derived from the matrices.

## Abstract

The reversible kinetics of copolymerization is solved analytically for the multistate mechanism proposed by B. D. Coleman and T. G. Fox [J. Chem. Phys. 38, 1065 (1963)] under low conversion conditions where the concentrations of monomeric species are chemostatted and stay constant in time. Although the rates of this mechanism only depends on the currently attached or detached monomer, the growing macromolecular chain forms a nonMarkovian sequence that is characterized by matrices associated with every monomeric unit composing the sequence. These matrices are obtained by solving the kinetic equations and they determine the growth velocity of the copolymers, the statistical properties of its possible sequences, as well as the thermodynamics of the copolymerization process.